The present invention relates to a sampled-data band-pass filter device, particularly adapted to be included in signal processing systems.
Usually, in order to perform band-pass filtering, "time-continuous" filters, of the passive type provided by means of capacitors, inductors and resistors, or of the active type provided by means of operational amplifiers, resistors and capacitors, are employed.
A per se known alternative method employs the so-called "sampled-data" technique; the signal to be filtered is first sampled and then subjected to the filtering process. Filters operating according to this method are known as "sampled-data filters". The literature provides a vast documentation on the problems related to the sampling of a signal and to its processing with the sampled-data method (e.g. "Digital Signal Processing", by A. V. Oppenheim and R. W. Schafer, Prentice-Hall, Inc., Englewood Cliffs, N.J., U.S.A., 1975).
An essential advantage provided by sampled-data filters resides in the fact that they allow a very accurate filtering action. Filtering specifications can in fact be provided with remarkable precision and in a manner substantially independent from environmental and/or operating conditions.
Moreover, such filters are very adaptable for monolithic integration.
A known phenomenon related to the sampling process is that it introduces in the spectrum of the signal some components which are the shifts of the spectral components of the original signal around the whole multiples of the sampling frequency. If M(.omega.) is the spectrum of a time-continuous signal m(t), the spectrum M.sub.s (.omega.) of the signal obtained by ideally sampling m(t) with a succession of pulses having an infinitesimal duration ("Dirac's delta") arranged at a distance T.sub.s from one another is given by: ##EQU1## where .omega..sub.s =2.pi./T.sub.s =2.pi.f.sub.s is the angular sampling frequency.
Actually, since the sampling process is not ideal, the spectral components are increasingly attenuated as .omega. increases, by the so-called "sin (x)/x factor". The real spectrum of the sampled signal M.sub.es (.omega.) is given by: ##EQU2##
If in the time-continuous signal m(t) there exist components of appreciable value at a frequency higher than f.sub.s /2, in the spectrum of the sampled signal there may thus appear, in the frequency interval 0-f.sub.s /2 (called "base band"), additional components with respect to those present, in said band, in the signal m(t). This phenomenon, known as "aliasing", makes impossible a correct "reconstruction" of the signal m(t) starting from the sampled signal (typically this is achieved by simple time-continuous low-pass filtering, which cuts the components at a frequency higher than f.sub.s /2).
The disadvantage of aliasing generally leads to the provision of a low-pass time-continuous filtering ("antialiasing") before the sampling, with the aim of eliminating all the unwanted components possibly present in m(t) at a frequency higher than f.sub.s /2. In order to avoid the need to have the antialiasing filter be very selective, and thus expensive, it is convenient that the components of actual interest of the signal m(t) be all at frequencies much lower than f.sub.s /2.
Though in most cases aliasing is a disadvantage, as will be described hereinafter, it is used as the fundamental principle of the invention described herein.
To provide an effective sampled-data processing device it is thus convenient to use, according to the prior art, a sampling frequency much higher than the signal's maximum frequency of interest. If it is required to perform a filtering on a high-frequency signal (e.g. a few MHz), it is necessary to use a very high sampling frequency (typically, in the example given, a few tens of MHz), which can be particularly difficult, expensive, or in some cases, for example when the filtering system is to be included in a monolithic integrated circuit provided with methods not allowing very high speeds, even impossible.
In some processing systems (e.g., in many reception systems) the signal is often shifted to a lower frequency range in order to simplify processing, in particular the filtering operations (in fact, it is easier to provide a low-frequency selective filter than a high-frequency one). A typical example is given by a "superheterodyne" receiver, wherein the frequency shift if achieved by means of a beat circuit, with which the signal to be processed is multiplied with a signal of adapted frequency (see e.g. H. Taub, D. L. Schilling: "Principles of Communications Systems", McGraw-Hill, Inc., New York, 1971, page 268 onwards). The addition of the circuit blocks required to perform this frequency shift logically entails a greater complexity and a greater overall cost of the system.